What you need to know
2D shapes can have what we call lines of symmetry. A line of symmetry is a line that you can draw through the shape such that what you see on one side of that line is a “mirror-image” of what you see on the other side.
Practically, this means that if you place a mirror along the line of symmetry, the reflection you see in the mirror will be exactly the same as the part of the shape that the mirror is blocking from view. In other words, placing a mirror on the line of symmetry with leave the shape perfectly intact.
To understand this, try it! Take a small mirror and hold it up along the lines of symmetry in some of the shapes below. You will see the result being, well…the same shape you started with!
Lines of Symmetry
Below are a selection of common shapes with their lines of symmetry shown as red, dashed lines.
As you can see, the equilateral triangle has 3 lines of symmetry whilst the square has 4. In general, we can say: the number of lines of symmetry for a regular polygon is equal to the number of sides.
Many shapes have no lines of symmetry at all, like the triangle shown below.
So, we can conclude that some triangle are symmetrical whilst some are not, this is true of other shapes as well, e.g. trapeziums. The trapezium on the left has 1 line of symmetry, whilst the trapezium on the right has none.
There’s no need to try to memorise all of these shapes and their lines of symmetry. Instead, get used to what a shape looks like when it is symmetrical, and try and find a small mirror you can use to have a go at these with!
1) State the number of lines of symmetry an isosceles triangle has.
The easiest way to answer this is to draw an isosceles triangle and see.
Your example might look quite different, but they all have the same number of lines of symmetry. Looking at the picture we can see it doesn’t have the full 3 that an equilateral triangle has, instead it has 1 – in our picture, a vertical line from top to bottom.
Indeed, any isosceles triangle will have 1 line of symmetry.
If we recall, a regular pentagon should have 5 lines of symmetry since it has 5 sides. Drawing all 5 lines on, we get the picture below:
3) Draw a shape with exactly 2 lines of symmetry. Include the lines of symmetry on your drawing.
There are endless possibilities for shape you could make with two lines of symmetry, the two most obvious answers being a rectangle and a rhombus.
What other shapes can you think of with 2 lines of symmetry?